5. Let f(x) = sin x cos x a) Determine the first derivative, and the second derivative. b) What is the third derivative? How can you find the fourth, fifth and sixth derivatives? Describe any patterns that you notice.

Q: 5. Use the Limits at Infinity Theorem and limit laws to evaluate lim f(z) where 818 16-² f(x)=…

A: fx=16-x26x2-5x+4

Q: Use the Shell Method to compute the volume of the solid obtained by rotating the region in the first…

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Q: Find the maximum rate of change of the function f(x, y) = DNE 2y² x at the point (2,4)

A: The function is given by fx, y = 2y2x The point is 2, 4 To evaluate: The maximum rate of change of…

Q: Draw the graph of the parametric curve defined by x(t) = 6 cos(t) and y(t) = 6 sin(t) below.

A: To draw the graph of the parametric curve defined by  xt=6 cost and yt=6 sint.

Q: Solve the following system of equations 2x + y = 1 3x + 1.5y = 1.5 Give a geometric…

A: To solve the following system of equations. 2x+y=13x+1.5y=1.5 To give a geometric interpretation of…

Q: Find the area of the triangle whose vertices are given below. A(-6,6) B(3,-2) C(11,-2) The area of…

A: Given: Triangle points:-  A(-6,6) B(3-2) C(11,-2)

Q: Write the trigonometric expression as algebraic expression in u. cot(cos^-1u)

A: We have to write the trigonometric expression as algebraic expression in u. cot(cos^-1u).

Q: Find the length of the curve. = (4t, r(t) = 4t, t2, 6 0 ≤t ≤1.

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Use the graph of the function f shown to the right to find f(-4), f(-3), and f(-2). f(-4)= f(-3) =…

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Q: Find an explicit solution of the given initial-value problem. x2dy dx =y-xy, y(-1) = -4 y =

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Q: When a body is freed from a FIXED SUPPORT, what support reactions must be used to replace the effect…

A: This is question of support reaction  Here fixed support is given  And free body diagram related we…

Q: In this problem, y=c₁ex + c₂e-x is a two-parameter family of solutions of the second-order DE y" - y…

A: Given that ,   y = c1ex + c2e-x  is  a solution of the differential equation y''-y =0. We have to…

Q: Evaluate the definite integral. 7 7 4 X X-5 X X-5 dx = dx

A: To evaluate the following definite integral. ∫47xx-5 dx

Q: In this problem, x = C₁ cos t + c₂ sint is a two-parameter family of solutions of the second-order…

A: We will find the general solution .

Q: Determine x = f(t) for dx (t² + 6t). dt = 6x + 6, t> 0; f(1) = 9.

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Q: (ii) (iii) Find the co-ordinates of the turning points of the following function: y = x³ - 6x² +5…

A: Given the equation, we need to find out the turning points of the curve and also where it has maxima…

Q: Consider the region bounded by the parabolas: y : x² + 4x + 3 and y = x² + 2x + 3. the volume of the…

A: Red graph is y=x2+4x+3 and blue graph is y=-x2+2x+3

Q: A man gets a job with a salary of 31800 dollars a year. He is promised a 2780 dollars raise each…

A:

Q: Find the area between the curve y = y 2.0 1.5 1.0 0.5 1 square units y = 2 1 x5/4 1 X5/4 3 and the…

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Q: 10. Given = [10,4] and = [12, 13], find the projection of u on v. -

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Q: Use the chain rule to find dz dt 11 dz dt = √t, y = ²/2 t z = sin(x) cos(y), x =

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Q: Assignment: Consider the region bounded by the parabolas: 2 2 y = x² + 4x + 3 and y = x + 2x + 3.…

A: We need to find volume.

Q: me Value Theorem, which of the following is true?   A) f(x) achieves a maximum f(c) and…

A: f(x)=x2

Q: Use the equations to find дz дх дz ду || || дz дх дz дх OF дх ƏF дz and and əz ду дz ду x2 - y2 + z²…

A: Given: ∂z∂x=-∂F∂x∂F∂z and ∂z∂y=-∂F∂y∂F∂zx2-y2+z2-8z=9 We are required to find: ∂z∂x and ∂z∂y

Q: əz дz Use implicit differentiation to find and Әх ду дz Әх дz ду = = II x2 - y2 + z² - 42 = 3

A:

Q: 5. Find f'(x) if f(x) = √4sin²x +9 cos²x. Solution: U= du dx B) Implicit Differentiation Example:…

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Q: Show every step to solve the problem. Solve question subpart D ONLY.

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Q: Set up an integral for the area of the shaded region. Evaluate the integral to find the area of the…

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Q: Evaluate the definite integral. [° ( Z - ²3/) dx J₁ X

A: ∫16x6-9xdx

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 3x sin(xy)…

A: To find:  the Direction in which the maximum rate of change occurs for f(x,y)=3xsin(xy) at point…

Q: Consider the graph of the function f. f(x) -10 -5 Yet 5 5 - 10 5 Use interval notation to determine…

A: As per our company guidelines we are supposed to solve first three subparts only please repost other…

Q: Use the chain rule to find dw dt = dw dt w = In (√x² + y² + z²), x = 8 sin(t), y = 7 cos(t), z = 2…

A:

Q: The three series Σ An, Σ Bn, and Σ C, have terms 1. 2. 3. Use the Limit Comparison Test to compare…

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Q: Find all values of m so that the function  y = xm  is a solution of the given differential equation.…

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Q: The radius of a right circular cone is increasing at a rate of 1.2 in/s while its height is…

A: given radius of a right circular cone is increasing at a rate of 1.2ins and height is decreasing at…

Q: Let a = (0, 1) and b = (4, -4). Show that there are scalars s and t so that sa + tb = (16, −17) You…

A: We have, a = ⟨ 0, 1 ⟩  b = ⟨ 4 , -4 ⟩ sa + tb =⟨ 16 , -17 ⟩

Q: 9. Find an equation of the tangent line to the curve x³ + y3 = 9 at the point (1.2). Solution:.. dx…

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Q: Evaluate. Use reduced fractions instead of decimals in your answer. 7 sec 6x dx = ² S + C

A:

Q: D. MEAN-VALUE THEOREM & ROLLE'S THEOREM Determine if Rolle's Theorem and the Mean Value Theorem is…

A: Note:- Since you asked multiple question , according to our policy we can solve only first question…

Q: 20. Which statement represents the relationship between P = {9, 11, 13, 15, 17) and Q = (2, 4, 6, 8,…

A: As per guidelines we are supposed to answer first question only please repost the Other question.

Q: This was for question D I did not need A,B,C

A: We need to compute the average rate of change of the future value of the account between year 9 and…

Q: Sketch the graph of the following parametric equations. a. x = 4, y = sint b. x = e^t, y = e^2t, t ∈…

A: a) x=4 ,y=sint b) x=et,y=e2t ,t∈[0,∞) c)x=3sint,y=4cost ,t∈0,pi

Q: /n³ + 1 n=1 3n³ + 4n² + 2 00 EXAMPLE2 Σ Since an is an algebraic function of n, we compare the given…

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Q: Recall the Chain Rule and how it can be applied to find the derivative of a composite function. In…

A: For each of the following functions, by using chain rule to find the  function's derivative. (i)…

Q: An Internet bookstore charges $20 shipping for orders under $100 but provides free shipping for…

A: C(x) = x + 20 if x < 100         =  x   if  x ≥ 100

Q: Find an explicit solution of the given initial-value problem. dy_y2. = y(7) = 7 y = dx حمد

A: Given: dydx=y2-1x2-1,y(7)=7 We are required to find: The value of y.

Q: graphs are given below. a) V Y b) Y = 10

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) [ sin (√x) dx

A: Given integral is ∫sinxx dx

Q: A function fhas a slant asymptote y = mx + b (m‡0) if lim [f(x) - mx + b] = 0 and/or lim [x)-mx + b]…

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Q: Water is leaking from a 2 foot tall rectangular tank at 0.1 cubic foot per hour. Suppose that the…

A: